An arrow with a mass of 30g is shot straight up to a height of 130m what is the arrow's initial velocity?
Potential energy at max height = (initial kinetic energy)
m g h = (1/2) m V^2
Cancel the m's and solve for V
ok thanks that is what i thought it might be but i just wanted to make sure. I also have another problem that i am hoping that you could help me with. A car requires 30 horsepower to move at a constant 20m/s what is the amount of friction that is needed to overcome?
To find the arrow's initial velocity, we can use the principle of conservation of energy.
The total mechanical energy of the arrow is the sum of its potential energy and kinetic energy. At the highest point, all of the arrow's initial kinetic energy will have been converted into potential energy.
Let's break down the problem step by step:
1. First, calculate the potential energy of the arrow at the highest point (130m):
Potential Energy (PE) = mass * acceleration due to gravity * height
PE = (0.03kg) * (9.8m/s^2) * (130m)
2. Since the arrow's velocity is zero at the highest point, its initial kinetic energy (KE) is also zero.
3. Since total mechanical energy is conserved, the initial kinetic energy is equal to the potential energy at the highest point. Therefore:
Initial Kinetic Energy (KE) = Potential Energy (PE)
4. Rearranging the equation for potential energy, we have:
KE = (0.03kg) * (9.8m/s^2) * (130m)
5. We can solve this equation for KE by substituting the known values:
KE = (0.03kg) * (9.8m/s^2) * (130m)
6. Now, we can find the initial velocity (v) using the formula for kinetic energy:
KE = (1/2) * mass * velocity^2
7. Rearranging the equation for kinetic energy, we have:
v = sqrt(2 * KE / mass)
8. Plug in the known values:
v = sqrt(2 * [(0.03kg) * (9.8m/s^2) * (130m)] / (0.03kg))
9. Calculate the result using a calculator:
v ≈ 63.47 m/s
Therefore, the arrow's initial velocity is approximately 63.47 m/s.